A metal sphere of radius R and specific heat C is rotated about an axis passing through its centre at a speed n rotation/second. It is suddenly stopped and 50% of its energy is used in increasing its temperature, then choose the correct statement(s) from the following?
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a
Kinetic energy used to raise the temperature of the sphere is 2π2n25MR2
b
Kinetic energy used to raise the temperature of the sphere is 5π2n3MR
c
The rise in the temperature of the sphere is 4π2n2R27C
d
The rise in the temperature of the sphere is 2π2n2R25C
answer is A.
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Detailed Solution
Kinetic energy of the sphere K=12Iω2=12×25MR2(2πn)2=45π2n2MR2Kinetic energy used to raise, the temperature =0.545π2n2MR2=25π2n2MR2∴ΔT=2π2n2R25C